The administration's proposal came in response to a Democratic offer Tuesday that would effectively increase the tax on gasoline by 13 cents a gallon and slap a 4 percent sales tax on other fuels.

It was the first time the White House has endorsed an energy tax, a potentially significant breakthrough in the marathon budget talks.

Negotiators are working to produce a package that will trim the federal government's debt by $500 billion over the next five years and its spending shortfall for fiscal 1991 by $50 billion. To that end, they planned to work into the night yesterday and continue until they either succeeded in reaching agreement or stumbled into deadlock.

Much of yesterday's session was spent discussing the makeup of tax increases needed to reduce the deficit. The negotiators have agreed to boost taxes by $25 billion next year and by $130 billion over the next five years. Serious disagreement remains over what taxes to raise.

According to an official present at yesterday's session, budget negotiators also discussed a proposal to raise the 16-cent-per-pack federal tax on cigarettes by 12 cents. The additional tax would be phased in over a five-year period: a 3-cent-per-pack increase at the enactment of the budget plan, a 3-cent increase two years later and a 6-cent increase the year after that.

The cigarette tax was advocated by Representative Dan Rostenkowski, D-Ill., chairman of the tax-writing House Ways and Means Committee, and Representative William Archer of Texas, the committee's top-ranking Republican. The phase-in was suggested by Sen. Wyche Fowler, D-Ga., who contended during yesterday's closed-door meeting at Andrews Air Force Base that influential lawmakers from tobacco-growing states would never support a budget package that raised cigarette taxes 12 cents in one year.

Similar concerns about regional opposition motivated the administration's petroleum tax proposal. Gasoline taxes of the sort suggested Tuesday by Democratic negotiators are generally supported in the densely populated regions of the North but are opposed by oil-producing states in the Southwest. Conversely, taxes on imported oil are supported by oil producers, whose own petroleum prices would soar as a result, and are opposed by the fuel-consuming states of the Northeast.

On the other hand, a broad-based petroleum tax -- one imposed on heating oil, gasoline, diesel fuel and other products -- hits producers and consumers alike in all parts of the country.

Negotiators have asked the congressional Joint Taxation Committee to generate estimates of the amount of tax revenue that would flow into government coffers as a result of such a tax -- as they have with the contemplated cigarette tax. Meanwhile, administration officials contended that, over five years, the levy would generate $7 billion for each 1 percent tax applied at the refinery.

The latest round of budget talks began last Friday, when budget negotiators abandoned the distractions of the Capitol for the comparative isolation of Andrews 10 miles away. Although participants expressed pessimism earlier this week about their ability to conclude an agreement, a series of subsequent small triumphs and breakthroughs have led some to predict a deal by the end of the week.

"We are still very, very far apart," said House Republican Whip Newt Gingrich of Georgia. "To borrow from Mark Twain, the reports of our success are greatly exaggerated."

But not, it turns out, the size of the deficit. Yesterday, Congress was informed that the deficit appears to be bigger than anyone had previously thought.

At a hearing of the Senate Banking Committee, Congressional Budget Office Director Robert Reischauer told the committee that the fiscal 1991 deficit now looks to be $30 billion to $35 billion larger than it did in June because of the weakening economy and rising oil prices. In June, Mr. Reischauer had predicted that the government's spending shortfall would hit $232 billion.